How do you simplify #cot^3x + cot^2x + cotx + 1# ?

1 Answer
Douglas K.
Feb 13, 2018

An alternate form which may or may not be considered simpler is obtained by factoring and then substituting #cot^2(x)+1 = csc^2(x)#

Explanation:

Given: #cot^3x + cot^2x + cotx + 1#

Factor:

#cot^2(x)(cot(x)+1) + 1(cot(x)+1)#

#(cot^2(x)+1)(cot(x)+1)#

Substitute #cot^2(x)+1 = csc^2(x)#:

#csc^2(x)(cot(x)+1)#

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